Linear Analysis of Feedforward Ring Oscillators

Multiphase clocks are very useful for realizing high-speed data processing systems with low-speed circuit elements. Triggered in sequence by equally-spaced N-phase clock signals, multiphase systems can achieve N-times higher operating frequencies than single-phase clocked systems. For this reason, multiphase clocks are often used for such applications as high-speed analog-digital converters (ADCs) and clock and data recovery (CDR) circuits. The ring oscillator (RO) structure is widely used for generating multiphase clocks. In feedforward ring oscillators (FROs) [1]–[7], feedforward signal paths are added between delay stages and can achieve much higher oscillation frequencies than conventional ROs without any feedforward paths [5], [6]. In addition, oscillation with an even number of single-ended delay stage [1], [3], [4], [7] can be achieved, which is not possible with conventional ROs. Although many different names have been used for FROs such as negative-skewed delay RO [1], coupled RO [3], and subfeedback RO [7], we will use the name FRO in this paper. FROs have been analyzed with several different methods. Well-defined models and equations are introduced in [2], [6], and the mechanism for the oscillation frequency enhancement characteristic of FRO is analyzed. However, these cannot predict oscillation modes. Consequently, oscillation frequency optimization based on these models is limited. In this paper, a generalized linear FRO model is developed, which can cover a wide variety of FRO structures. The model allows prediction of multiple oscillation modes and oscillation frequencies. The accuracy of the model is verified with transistor-level simulation.